Technical details for developing a biochronology (click on the "Definitions" link above) are described in the references below. These papers are a bit esoteric in the statistics, possibly necessary to get past the reviewers and editors, but too complicated for quick digestion. The following encapsulation of ideas should provide enough information for you to evaluate whether or not this technology might be useful for your particular application.
Starting with the Weisberg paper (CJFAS, 1993), the basic procedure
is to measure growth increments on scales or otoliths (or other
parts) and to set up a statistical model that postulates that
a single increment is the simple sum of growth due to the peculiar
characteristics of the calendar year in which it was laid down,
plus growth due to the age (size) of the fish at the time the
increment was laid down. The first component of this increment
we call "year" effect, the second is the "age"
effect. Now that we can separate growth increments into these
two components, it is possible to speculate that the "year"
effect includes environmental conditions that prevailed during
a particular year, including things such as temperature, or food
supply or density, or other things that influence density-dependent
growth. So, in a good year, after we have subtracted the age effect
for a particular fish (sample) we would expect to see a large
increment left over. In a poor year, the increment would be very
much smaller. In Weisberg's paper (smallmouth bass) an example
of a good year is 1984 (Fig. 2) whereas 1985 and 1986 were very
poor growth years. The statistics are really no more complicated
than fitting a linear model to the increment data. Weisberg has
written a program that does the fitting, and the University
of Minnesota Sea Grant program sells it for a modest fee--$25?
The data setup is similar to the file structure that is specified
for the DisBCAL program (Frie, 1982) that the Missouri Dept. Conservation
has distributed for years (now available from the American
Fisheries Society Computer Users Section web site).
The next step in developing a master chronology is to use the
increment analysis to piece together a history of year effects,
or, "biochronology." This is best done by sampling fish
from a particular site every year, or, at least every few years
so that the older fish in your sample will cover the gaps in years
that were not sampled. This is the reason that very old fish are
valuable for biochronology. They contain a record of year effects
that covers a long period. If you have several fish from different
time periods that shared a few years of their lives as contemporaries,
then you can put together a longer history for the lake they inhabited.
This is the procedure that dendrochronologists call "cross-matching"
in splicing together tree ring histories. Eventually, you can
develop a biochronology for a particular species of fish that
spans a considerable number of years. This is what we have done
in the Pereira et al. (1995) Otolith Symposium paper, where we
have otolith growth increments from freshwater drum that date
back to the 1878 year-class (figs. 2A and 2B). The statistical
models fitted to these increments are on p. 185 in that paper,
but the biochronology that is the result appears in the upper
panel of figure 6. This saw-toothed pattern of "year"
effects is the residual variation left over in the growth increments
after the effects of age have been subtracted from the fish's
growth record. In this paper, we are calling this plot "growth
index three," or GI3. WHAT'S THE BIG DEAL? Well, maybe it
isn't a big deal, but, the bottom panel in fig. 9 shows GI3 with
a series of black dots in certain years after 1919. These dots
correspond to the years which produced outstanding year-classes
of freshwater drum in the Red Lakes of Minnesota. I don't think
it is just coincidence that the best year-classes ever seen, 1955,
63, 70, 83, and 87 (and probably 1878, 1886 and 1919 too) occurred
in years having the best growth indices. In fact, 60% of the 1989
catch of drum from Red Lake, approximately 1/4 million lbs, consisted
of fish of the 1970 year-class. Imagine how many there must have
been for that number to have reached the ripe old age of 19! So,
this gives us some support for the idea that we can find strong
environmental signals in the growth increments depicted by these
biochronologies.
The Pereira et al. (1995) paper in the climate change symposium does not make a statistically persuasive case for detecting large-scale climate effects in the growth of drum in mid-continent. But the analyses are greatly compromised by constraints on the time series of weather data available and on the arbitrariness of things like interval choice in the superposed epoch analyses. In spite of the statistical complications, it is clear that drum year-classes in Minnesota's latitudes depend greatly upon the occurrence of warm summers.
We intend to pursue the biochronology research with freshwater
drum because of their natural distribution all the way from Guatemala
to Hudson's Bay. With such a breadth of geographic latitudes,
we should be able to sort out major climatic effects if we can
put together a biochronology for several sites spaced 5 or 10
degrees of latitude apart.
What else are biochronologies useful for? We think the major use
will be as an aid to determining the age of fishes from their
bony parts. This is the idea of specific periods of time generating
"temporal signatures" in the growth increments of their
bony parts. The best fit of a particular fish's growth increments
to a master chronology may assist in assigning that fish to a
specific year-class. See the animation
of this process prepared by Derek
Ogle . For more information on temporal signatures
follow this link, or continue reading below.
Frie, R. V. (1982). Measurement of fish scales and backcalculation of body lengths using a digitizing pad and microcomputer. Fisheries, 7, 5-8.
Pereira, D. L., Bingham, C., Spangler, G., Cohen, Y., Conner, D., & Cunningham, P. (1995). Growth and recruitment of freshwater drum (Aplodinotus grunniens ) as related to long-term temperature patterns. Can. Spec. Publ. Fish. Aquat. Sci., 121, 617-629.
Pereira, D. L., Bingham, C., Spangler, G., Conner, D., & Cunningham, P. (1995). Construction of a 110-year biochronology from sagittae of freshwater drum (Aplodinotus grunniens ). In D. H. Secor, J. M. Dean, & S. Campana (Eds.), Recent Developments in Fish Otolith Research, (Vol. 19, pp. 735). Columbia: The Belle W. Baruch Library in Marine Science, University of South Carolina Press.
Weisberg, S. (1993). Using hard-part increment data to estimate age and environmental effects. Can. J. Fish. Aquat. Sci., 50(6), 1229-1237.
We think that one major use for biochronologies (based upon incremental growth of hard parts of fishes) will be as an aid to determining fish ages in connection with population studies. This is the idea of specific periods of time generating "temporal signatures" in the growth increments of bony parts. The drawback to this is that you have to have a biochronology (see heading of that name on home page) to begin with, but let's deal with that in a minute. Here's how the thing works. Suppose you do have a biochronology for your favorite fish species from a particular place, say, Lovewell Reservoir, Kansas, on the Republican River system (Is it true that a certain senator from that state has proposed a name change for the reservoir to something reminiscent of a salamander?). Suppose the biochronology runs from 1960 to 1990, and you have just caught (in 1995) a smallish (5 kg?) flathead catfish (Pylodictus olivaris ). You measure the growth increments on the spine cross-sections, run them through a linear model program (Weisberg, 1993) to separate out the year-effects, then plot them as a jagged pattern, much like the GI3 pattern (only much shorter) in fig. 9 of Pereira, et al. (1995--Otolith Symposium). Now, all you have to do to ascertain the age of your fish is to "slide" its own saw-tooth pattern alongside the master chronology that you have developed for Lovewell Reservoir, until the best match is found to the master chronology. Voila! The age of the fish is the difference between 1995 (when you caught the fish) and the first year of the series of years that best match your fish. This is simple to do graphically if you have a graph of every fish's growth increments, and, in fact, that is how the dendrochronologists match up various periods in the history of forest growth based on tree rings. For fish it is a bit more of a statistical problem. In Ogle et al. (1994), we show a statistical method for successively comparing an individual fish's growth increments with every possible position along a master chronology. We used growth increments on scale samples from Red Lakes walleye (Stizostedion vitreum ). The point in the series where there is a minimum sum of squares of the deviations between the master chronology and the fish's individual pattern is judged to be the point of best match. From this we assign a probability that the fish belongs to such-and-such a year-class. The advantages of this method over the standard approach of looking at scales or rings on spines or otoliths is that we can automate the process, assign a specific probability for membership in a particular year-class, and, more importantly, the age analyst doesn't have to see a complete record of growth. If the last few increments are not visible on the scale because of resorption or erosion of the outer edge, all is not lost. From the matching of the first 6-8 increments, we can still determine which era best corresponds, and assign an age to the fish. Getting the master chronology is a bit of work, and it requires some maintenance sampling, although annual sampling may not be necessary. The original master chronology may not be very precise, but it will improve in quality with age as more years of data are tacked onto the most recent end of it. It can initially be based on known-aged fish, or very young fish that you can age confidently from scales or spines.
Well, that is probably more about biochronology and temporal signatures
than you may ever want to know, but it sums up why we are interested
in developing the technology further. There is no reason not to
use the method for other species too, including invertebrates,
if they can be aged. So far, we have developed biochronologies
for freshwater drum (Aplodinotus grunniens , Pereira's
papers) and walleye, Stizostedion vitreum , (Ogle et al.,
1994; Cyterski, 1995), shallow-water cisco, Coregonus artedii,
from Lake Superior (Krause, 1999) and lake trout (Salvelinus
namaycush ) from Lake Superior. I suspect these methods will
be useful for a host of fishes that show density-dependent growth,
perhaps even for flathead catfish!
Cyterski, M. J. (1995). A Growth History of Red Lake Walleye (Stizostedion vitreum ) Developed Through Scale Analysis. M. Sc. Thesis, Dept. Fisheries and Wildlife, University of Minnesota. 140 pp.
Frie, R. V. (1982). Measurement of fish scales and backcalculation of body lengths using a digitizing pad and microcomputer. Fisheries, 7, 5-8.
Ogle, D. H., Spangler, G. R., & Shroyer, S. M. (1994). Determining fish age from temporal signatures in growth increments. Can. J. Fish. Aquat. Sci., 51(8), 1721-1727.
Pereira, D. L., Bingham, C., Spangler, G., Cohen, Y., Conner, D., & Cunningham, P. (1995). Growth and recruitment of freshwater drum (Aplodinotus grunniens ) as related to long-term temperature patterns. Can. Spec. Publ. Fish. Aquat. Sci., 121, 617-629.
Pereira, D. L., Bingham, C., Spangler, G., Conner, D., & Cunningham, P. (1995). Construction of a 110-year biochronology from sagittae of freshwater drum (Aplodinotus grunniens ). In D. H. Secor, J. M. Dean, & S. Campana (Eds.), Recent Developments in Fish Otolith Research, (Vol. 19, pp. 735). Columbia: The Belle W. Baruch Library in Marine Science, University of South Carolina Press.
Weisberg, S. (1993). Using hard-part increment data to estimate age and environmental effects. Can. J. Fish. Aquat. Sci., 50(6), 1229-1237.
Archaeometry refers to the use of archaeological material
for the chronological dating of historical sites. Cultural artifacts
and fossil remains of plants and animals have traditionally been
used to ascertain both relative and absolute dates for excavated
sites. Dendrochronology,
the science of tree ring analysis, has been a widely successful
archaeometric tool for determining dates and durations of site
occupation by human inhabitants.
Dendrochronologists create master chronologies by matching and
overlapping similar growth sequences among tree cores. A chronology
is extended back in time by the successive addition of older and
older trees. Excavated tree remains such as petrified lumber,
charcoal pieces, and prehistoric wooden tools are then compared
to these master tree chronologies in order to place archaeological
materials in time.
This same technology is now being applied to the field of biochronology.
Growth increment sequences recorded within calcified, bony structures
of aquatic organisms (e.g. fish scales and ear stones, vertebral
bones, mussel shells) contain "otoliths (ear stones) found in historical
Indian middens. 
These techniques include detrending methods for removing the effects of age on growth, filtering methods for clarifying environmental signals, and correlation methods for matching portions of contemporaneous growth histories.
After individual otolith growth series have been cross-matched
in time, a master chronology can be constructed which represents
annual growth for an historical fish population during a specific
time period. For validation of accuracy, horizontal positions
of individual growth series along the chronology should correspond
to vertical placement of otoliths within midden strata.
By anchoring this undated "floating" chronology to
a dated series (such as a master tree chronology or historical
temperature records), specific calendar years can be assigned
to points within the chronology. 
This
information can then be used to determine both the dates and duration
of occupancy for inhabitants using the midden sites. In addition,
information regarding structure of the fish population (e.g. ages
and sizes of individuals, growth parameters) can be obtained from
this analysis for comparison to modern populations.
The term "BIOCHRONOLOGY" is applied here to mean "the use of organic growth increment patterns in the body parts of aquatic animals to discern events experienced during the lives of those animals." This term has also been applied to the study of the fauna and flora of specific geologic time periods. Definitions of "biochronology" from some dictionaries include: 1): "The dating of biological events using biostratigraphic or palaeontological methods." (Lincoln, et al. 1982); 2) "The measurement of units of geological time by means of biological events" (Allaby 1991). Associated with evolutionary history are related terms such as "biochrons," or defined units of time in the past. We believe our use of the term will not mislead most biologists, although evolutionary biologists and palaeontologists are undoubtedly accustomed to thinking in terms of more temporally distant events.
Our use of "biochronology" is analogous to the term "dendrochronology" in forestry. Though broadly understood among biologists, this term too has many specific definitions, for example: 1) "A method of dating using annual tree-rings; tree-ring chronology" (Lincoln, et al. 1982); 2) "Science of reconstructing past climates from the information stored in tree trunks as annual radial increments of growth" (Walker 1989); 3) "The study of annual rings in timber to discover the age of the wood and the climatic situation at the time of growth" (Hale and Margham 1991). These definitions include elements of "dendroclimatology," "chronometry" and may convey other connotations as well. Because fish provide bones and other scales, and otoliths as useful structures for age interpretation, the term "osseochronometry" has been proposed for interpretive studies of these structures. Clearly variations such as "microchronology," "otochronology," "microclimatology," and others come to mind as somewhat reasonable choices (see Casselman (1974) for a review of terms applied to deciphering age). I prefer the simpler "biochronology" to serve in our interpretations of the calcified structures of aquatic organisms as it seems sufficiently general to include most of the usages that I currently anticipate, and, it relates closely enough to "dendrochronology" to be quickly understood by most professional biologists.
You will undoubtedly note that we are anticipating application of our methods to aquatic organisms other than fishes. Molluscan shells depict clear growth increment records comparable to those in fish scales and otoliths. We hope to see a wide variety of applications of biochronology. Certainly, climatology, both macro and micro, age determination, and ecological inferences are among the many applications that we expect to emerge from consideration of these calcified growth histories recorded by the organisms. Lamprey statoliths and perhaps other biological structures may also be found useful in biochronological analyses. Our application of the term seems also to fall within at least some of the definitions corresponding to prior use of the term in the biological literature, although we will clearly not be applying it to "geologic time scales." We also anticipate temporal records that may range from hours or days to weeks, decades, or centuries. Thus it seems pointless to restrict definitions of this term to structures, organisms, or time scales that have already proven useful in ecological, phylogenetic or temporal analysis. For examples of more traditional uses of the term "biochronology" you may wish to search the Web for references to "paleobiology."
Allaby, M. (Ed.). 19991. The Concise Oxford Dictionary of Zoology. Oxford University Press, Oxford: 508pp.
Casselman, J. M. 1974. Analysis of hard tissue of pike Esox Lucius L. with special reference to age and growth In T. B. Bagenal (Ed.). The Ageing of Fish -- Proceeding of an International Symposium. Unwin, England.
Hale, W. G. and J. P. Margham. 1991. Harper Collins Dictionary of Biology. Harper Perennial, New York: 569pp.
Lincoln, R. J., G. A. Boxshall and P. F. Clark. 1982, A Dictionary of Ecology, Evolution and Systematics. Cambridge University Press, Cambridge: 298pp.
Walker, P. M. B. (Ed.). 1989. Chambers Biology Dictionary.
Chambers-Cambridge, Cambridge: 324pp.
A. B. Coffin (formerly Krause), University of Minnesota (Now, University of Maryland)
The standard biochronology computer routine by Weisberg fits
only one type of covariance matrix, an identity matrix that assumes
consecutive growth increments are uncorrelated. This assumption
is often invalid, so alternate covariance matrices are necessary.
The procedure MIXED in SAS (SAS Institute, Inc., 1997) can be
used to fit the linear growth model and produce parameter estimates
for chronology development using a variety of covariance matrices.
To use SAS, data files should be formatted according to
this file fragment:
YEAR ID GYEAR AGE
GROWTH
1983 10075 1979
1
0.5704
1983 10075 1980
2
1.4722
1983 10075 1981
3
1.0191
1983 10075 1982
4
0.8462
1983 10060 1980
1
0.6776
1983 10060 1981
2
1.5478
1983 10060 1982
3
0.6219
1983 10039 1979
1
0.4028
1983 10039 1980
2
1.0979
1983 10039 1981
3
1.0745
1983 10039 1982
4
0.4394
YEAR is the sample collection year. ID is the sample number for a specific scale within the collection. GYEAR represents the growth year. AGE is the age of the fish during that specific year. GROWTH is the growth increment for that specific fish in the growth year. Files may be created in spreadsheet software, then imported into SAS using the "import" command under the "file" menu.
The following code will fit the additive model (Weisberg 1993)
with an identity covariance matrix, identical to the model fit
produced by Weisberg's stand-alone program. Line numbers
are included for clarity only; they are not used when keying
code into SAS.
(1)Proc mixed data=dataset method=ml scoring;
(2)Class id age gyear;
(3)Model growth=age gyear / s;
(4)Repeated / type=un subject=id r;
(5)Run;
Line one specifies the type of SAS procedure to use (mixed model), and tells the program what data set to analyze. The variable dataset should be replaced with the name of the work file in SAS. Line two defines the variables. Variable definitions are given above. Line three lays out the model (in this case, equation 1). The "type=" statement in line (4) specifies the covariance matrix. We have used "un" which stands for uncorrelated. This choice assumes that all increments are uncorrelated with the same error variance. SAS permits several other choices as well. For example, the statement type= "CS" designates a correlation matrix that allows for constant correlation between successive growth increments. "AR(1)" indicates an autoregressive matrix, allowing for non-constant correlation between successive increments. The most general choices is an unstructured covariance, estimating a separate variance for each age and separate covariances for each pair of increments. We do not recommend use of this choice, as it fits many parameters for little added generality, and it often leads to computational difficulties. All the choices available are given in SAS Institute, Inc 1997.
The model including the interaction term may be fit
by changing line (3) to read:
Model growth=age gyear age*gyear / s;
A multiplicative model growth model can be fit by changing line
(3) to read:
Model growth=age*gyear / s;
All equations are explained in Weisberg (1993).
There are few practical limitations on the form of the mean
functions that can be fit using Proc Mixed. For example,
one could fit separate parameters for males and females, separate
year coefficients for different stocks of fish while fitting
common age parameters, and so on. The main drawback to
fitting models in SAS is the lack of graphical output.
SAS output may be saved as rich-text (.rtf) files, and these
files imported into a graphing program such as JMPin (SAS Institute,
Inc. 1996). The following fragment displays the graphical
output for a model fit with an autoregressive correlation matrix:
Effect
Estimate Std Error
DF t Pr > |t|
INTERCEPT
0.04786161 0.03457761 244
1.38 0.1676
AGE 1
0.13626244 0.02638315 697
5.16 0.0001
AGE 2
0.31871667 0.02710618 697
11.76 0.0001
AGE 3
0.25518701 0.02775453 697
9.19 0.0001
AGE 4
0.10374374 0.02762319 697
3.76 0.0002
AGE 5
0.00000000
GYEAR
1978 0.35773428 0.06713384
697 5.33 0.0001
GYEAR
1979 0.63181576 0.05831419
697 10.83 0.0001
GYEAR
1980 0.60502639 0.05000098
697 12.10 0.0001
GYEAR
1981 0.66282492 0.04266972
697 15.53 0.0001
GYEAR
1982 0.48537095 0.04172922
697 11.63 0.0001
GYEAR
1983 0.64860485 0.03952931
697 16.41 0.0001
Sample Files:
Detailed instructions for model fitting in XLISP-STAT may be found in Weisberg (1992). All XLISP files are text files.
1983 1984 1985
1986 1987
1988 1989
1990 1991
1992
Master File
References
Krause, A.B. 1999. Stock-specific growth rates of cisco (Coregonus artedi) in the Lake Superior environment. Master's Thesis, University of Minnesota, St Paul. 111 pages.
SAS Institute, Inc. 1996. A guide to statistics and data analysis using JMP and JMP IN software. Wadswoth Publishing Company, Belmont, California.
SAS Institute, Inc. 1997. SAS/STAT software changes and enhancements through release 6.12. SAS Institute, Inc. Cary, North Carolina.
Weisber, S. 1992. A computer program for using hard-part increment data to estimate age and environmental effects in fish populations. For: University of Minnesota, Department of Applied Statistics. 17 pages.
Weisberg, S. 1993. Using hard-part increment data
to estimate age and environmental effects. Can. J. Fish.
Aquat. Sci. 50:1229-1237.
Last updated on January 30, 2000.
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Date created: October 25, 1995 Last modified: June 2, 2000 Copyright © 1995, 1996, 1997, 1998, 1999, 2000 George Spanglergrs@finsandfur.fw.umn.edu
